Magnetotail Ion Structuring by Kinetic Ballooning‐Interchange Instability

Abstract By combining three‐probe THEMIS observations and 3‐D Particle‐in‐Cell simulations, we identify key structures on the ion gyroradius scale that occur in connection with ballooning‐interchange instability heads in the Earth's magnetotail. The mesoscale structures occur at sites of strong ion velocity shear and vorticity where the thermal ion Larmor radius is about half of the width of the head. Finer structures occur at the smaller scales characterizing the wavelength of the electromagnetic ion cyclotron waves generated at the heads. These two processes act to erode and thin the current sheet, thereby forming a local magnetotail configuration that is favorable for reconnection.


PIC Simulation Setup
The present investigation employs a 3-D PIC simulation model that retains the full dynamics for both electrons and ions. The initial magnetic field configuration is similar to those considered previously in Coroniti, 2010, 2013] and is described by the vector potential A 0y (x, z) given by where F(x) is a slowly varying but otherwise arbitrary function. For a nonconstant F(x), there is a finite B z field, which at the center of the current sheet has the form The specific configuration used in the present study is illustrated in Figure S6. Figure S6a shows the 2-D (x, z) magnetic field configuration, and Figure S6b shows the initial equatorial magnetic field profile B 0z (x, 0). The BICI modes will be excited in the region of the tailward gradient in B z (20 < x/ρ i0 < 28), which corresponds to a region of decreasing entropy as x increases tailward [Schindler and Birn, 2004;Pritchett and Coroniti, 2013].
Here, ρ i0 is the ion gyroradius in the asymptotic lobe B 0 field.
Previous PIC simulations of BICI generation Coroniti, 2010, 2013;Pritchett et al., 2014] have considered a charge neutral, generalized Harris configuration in which the ion and electron cross-tail drifts are given by V di = −2cT i /eB 0 L and V de = 2cT e /eB 0 L, where e is the magnitude of the fundamental electric charge and L is the halfwidth of the current sheet. In the present study, we consider a charged current sheet in which the electrons carry all of the cross-tail current with a net drift of V ch de = 2c(T i + T e )/eB 0 L. Since the ions now carry no current, an electric field E 0z (x, z) must be present in order to balance the nonuniform ion pressure, The (ion) density distribution is given by where n 0 is the characteristic equatorial density at x/ρ i0 = 16 and n b = 0.08n 0 is a constant background density. The density distribution for the current-carrying electrons is similar to that for the ions but with a larger characteristic density n e given by (n e − n 0 )/n e = [T i /(T i + T e )](V ch de /c) 2 . The simulation has a grid N x × N y × N z = 512 × 1024 × 256 distributed over the ranges 0 ≤ x/ρ i ≤ 32, 0 ≤ y/ρ i0 ≤ 64, −8 ≤ z/ρ i0 ≤ 8, so that ρ i0 = 16∆, where ∆ is the grid spacing. The ion to electron mass ratio is m i /m e = 64, all particle temperatures are equal to m i V 2 A /4 (here V A = (B 2 0 /4πn 0 m i ) 1/2 is a representative Alfvén speed), the electron plasma frequency/gyrofrequency ratio is √ 2, and the electron Debye length is ∆. The total number of particles in the simulation is 5.8 billion.
The simulation employs "closed" boundary conditions at the x boundaries [Pritchett and Coroniti, 1998]. No magnetic flux is allowed to cross these boundaries, corresponding to the condition δE y = 0, and particles that cross these boundaries are reinserted back into the system in the opposite half z plane with v x = −v x and v z = −v z [Pritchett et al., 1991]. In addition, the perturbed field δE z is assumed to vanish at these boundaries. At the z boundaries, conducting conditions are assumed, and particles striking such a boundary are reintroduced in the opposite half z plane with v x = −v x and v z = v z . This symmetric condition on the particle reflection is valid in the absence of a guide magnetic field. Periodicity in the y direction is assumed for both the particles and fields. The coordinate system used in the simulations has x increasing tailward (away from the Earth), y directed dawnward, and z directed northward. In the simulation figures, the coordinates are expressed in units of ρ i0 .
Caption for Movie S1.
Results from 3D PIC simulation of BICI development in the electron (charged) current sheet as seen in B X (a), B Y (b) and B Z (c) magnetic field components, ion density (d), kinetic ion energy density (e), T X X (f) and T XY (g) ion temperature components, P XY ion pressure tensor component (h), off-plane ion vorticity component ω iz (i), and inplane ion divergence ∂V iX /∂ x + ∂V iY /∂ y (j) between Ω i0 t=161 and Ω i0 t=280. The contours of B Z magnetic field component are overplotted as black curves. The star glyphs at (x/ρ i0 ,y/ρ i0 ,z/ρ i0 )=(10.5,23.0,-1.5) (magenta), at (x/ρ i0 ,y/ρ i0 ,z/ρ i0 )=(12.5,22.0,-1.5) (blue) and at (x/ρ i0 ,y/ρ i0 ,z/ρ i0 )=(13.5,20.5,-1.5) (cyan) denote the location of three virtual spacecraft also discussed in Figure 3 of the manuscript. and ESA (burst mode) ion differential flux spectra, azimuthal (PHI; 0 degrees corresponds to the Earthward direction) angle of ion motion, spacecraft potential (a high-resolution proxy to electron density), parallel component of the ion temperature (red), GSM V X ion velocity component, DSL E Z (red), E Y (green) and E X (blue) electric field components 3s-long-sliding-window averaged, GSM B Z (red), B Y (green) and B X (blue) magnetic field components. and ESA (burst mode) ion differential flux spectra, azimuthal (PHI; 0 degrees corresponds to the Earthward direction) angle of ion motion, spacecraft potential (a high-resolution proxy to electron density), parallel component of the ion temperature (red), GSM V X ion velocity component, DSL E Z (red), E Y (green) and E X (blue) electric field components 3s-long-sliding-window averaged, GSM B Z (red), B Y (green) and B X (blue) magnetic field components. and Ω i0 t=250 as seen in (from top to bottom) three magnetic field components and in the total magnetic field (B x , B y , B z , B t ), X and Y ion velocity components V ix and V iy , ion density N i , average ion temperature T i , nondiagonal ion temperature and ion pressure tensor elements T ixy and P ixy . In the simulation, the X axis is directed antisuward and the Y axis is dawnward, which is opposite to the GSM X and Y axes. The three curves correspond to the location of three virtual spacecraft at (x/ρ i0 ,y/ρ i0 ,z/ρ i0 )=(10.5,23.0,1.5) (magenta), at (x/ρ i0 ,y/ρ i0 ,z/ρ i0 )=(12.5,22.0,1.5) (blue) and at (x/ρ i0 ,y/ρ i0 ,z/ρ i0 )=(13.5,20.5,1.5) (cyan), i.e. at the same X and Y positions as in the left column of Figure    and ESA (burst mode) ion differential flux spectra, azimuthal (PHI; 0 degrees corresponds to the Earthward direction) angle of ion velocity, parallel (red) and perpendicular (blue and green) components of the ion temperature, three GSM components of the ion velocity V i , three diagonal GSM components of the ion pressure tensor P xx (blue), P yy (green) and P zz (red), spacecraft potential (a high-resolution proxy to electron density), and three GSM components of the magnetic field.